Two FRT bialgebroids and their relations

TL;DR

This paper generalizes the FRT construction to quiver-theoretical quantum Yang-Baxter equations, resulting in a new left bialgebroid and exploring its relations with existing structures.

Contribution

It introduces a generalized FRT construction for quiver-theoretical quantum Yang-Baxter equations and establishes relations between new and existing bialgebroids.

Findings

Construction of a new left bialgebroid $rak{A}(w)$

Relations established between $rak{A}(w)$ and $A_{\sigma}$

Extension of FRT framework to dynamical Yang-Baxter maps

Abstract

We generalize the FRT construction for the quiver-theoretical quantum Yang-Baxter equation and obtain a left bialgebroid $\mathfrak{A}(w)$. There are some relations between the left bialgebroid $ \mathfrak{A}(w)$ and a left bialgebroid $A_{\sigma}$ by the FRT construction for the dynamical Yang-Baxter map.